Edge

In graph theory, an edge ^[1][2] is one of the fundamental objects making up a graph, together with the vertices it connects. Each edge joins together a pair of vertices. The edges of a graph $G$ form its edge set $E(G)$.

Definition

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Definition 1 (Edge)

Let $G$ be a graph with vertex set $V$. An edge is a pair of vertices $u,v\in V$ that are joined together. The vertices $u$ and $v$ are called the endpoints of the edge. Two vertices joined by an edge are called adjacent, and the edge is said to be incident to each of them.

Variants

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Edges come in two basic variants, depending on whether the connection between vertices carries a direction:

• Undirected edge $\{u,v\}$: connects two vertices symmetrically, with no distinction between them. Both endpoints $u,v$ are simply called endpoints.
• Directed edge $(u,v)$: connects an ordered pair of vertices. The two endpoints are distinguished by name as the tail $u$ and the head $v$.

References

1. [1]

   “Glossary of graph theory”, Wikipedia, Available: https://en.wikipedia.org/wiki/Edge_(graph_theory), Accessed: 2026-07-14 ↩

2. [2]

   “Graph Edge”, Wolfram MathWorld, Available: https://mathworld.wolfram.com/GraphEdge.html, Accessed: 2026-07-14 ↩